Is there a symbol or flag for Democracy or a Democratic Republic?
This would be something general, not for a political party or country (unless the country happened to adopt a general symbol).
Regime types are abstractions. They don't have symbols, because they aren't "real" - just a convenient way for us to think about the kinds of political structures that may exist. So the easy answer to your question is, "no, there is no symbol for a democracy."
However, political groups may use symbols. If those political groups are advocating for a certain regime type there may be some symbols that in the public's mind come to be associated with that kind of regime. The symbol won't be broadly tied to the concept, but within a specific cultural context the two will be recognizably linked. One example is the red star. Due to its usage by Russian revolutionaries and subsequent adoption by the Soviet Union (as well as some other revolutionaries with somewhat similar ideals) it is tied to a very narrow notion of communism for a group of people in certain times and places.
Similarly, you can find some symbols which are tied to democracies or democratic republics. Examples:
These are just a few easy examples. Note that all of them are bound to a certain cultural context. While the silhouette of the rotunda makes sense to me (as a contemporary American), it likely wouldn't mean anything to someone from another country.
Often an image of the architectural building in which legislative deliberations take place is symbolic of democracy.
An image of a ballot box or ballot is also often sometimes used for this purpose.
Hands, or clasped hands are another common image.
But, as a Google image search of the term "democracy", reveals, there is really no single consensus image that captures the concept.
I've seen stylised Greek ruins / pillars used for this purpose. Or to symbolise civic engagement in general - of which democracy is the most significant format inherited from the Greeks and Romans.
Most other representations on the internet tend to be due to the extent of American political artefacts. Although the USA has a rightful claim to the symbol of a republic since most countries outside of Europe that transitioned away from a monarchy opted for a republic-style democracy.
Many republics have a star as their symbol.
Communist governments often call themselves "Democratic Republics" or "People's Democratic Republics". These governments often have either a red star, or a white or yellow star on a red field, as their symbol. The Soviet Union's symbol was a yellow hammer crossed with a yellow sickle, on a red field.
It has often been noted that the more redundantly a government name claims to be popular, democratic, and republican, the less likely the government is to be any of those things.